This story has been updated to include comments from White House press secretary Josh Earnest and House Speaker Paul Ryan.

WASHINGTON — President-elect Donald Trump met with President Barack Obama, House Speaker Paul Ryan and other top GOP leaders today to discuss the upcoming transition between presidential administrations.

After Trump's meeting at the White House, both he and Obama described their discussion as positive, expressing optimism that the massive logistical challenge of a presidential transition would go smoothly.

"My No. 1 priority in the coming two months is to try to facilitate a transition that ensures our president-elect is successful," Obama told reporters. "I believe that it is important for all of us, regardless of party and regardless of political preference, to now come together, work together, to deal with many of the challenges we face."

"We discussed a lot of different situations, some wonderful, and some difficulties," Trump said. "I very much look forward to dealing with the president in the future, including counsel."

"He's explained some of the difficulties, some of the high-flying assets, and some of the really great things that have been achieved," Trump added.

In the 70 days before Trump's inauguration, his transition team will need to fill thousands of jobs across federal agencies while ensuring that national security does not waver during the handoff. According to a New York Times report, the Obama administration will hold two war-gaming exercises to prepare Trump and his staff for any national security crisis that might unfold once Trump takes the reins in January.

The discussion between Obama and Trump was the first meeting between the two men, neither of whom has been shy about criticizing the other. For years, Trump sought to cast doubt on Obama's legitimacy as president, sowing doubts that the nation's first black president had been born in the U.S.

Obama, who campaigned vigorously for Hillary Clinton, said on many occasions that progress his administration has made would "go down the drain" if Trump were elected. Before the election, when reports surfaced that members of Trump's campaign had "wrestled away" control of Trump's private and often inflammatory Twitter account, Obama mocked Trump on the campaign trail.

"If your closest advisers don't trust you to tweet, then how can we trust him with the nuclear codes?" Obama asked crowds.

White House press secretary Josh Earnest acknowledged previous tension between the two men but reiterated that Thursday's meeting went smoothly.

"I feel confident in telling you that they did not resolve all their differences," Earnest told reporters. "I also feel confident in telling you they didn't try to resolve all their differences.

"What they sought to do is lay the foundation for an effective transition," Earnest added. "Based on the kind of agreement that was evident, about the priority they both place on a smooth transition, it sounds like the meeting might've been a little less awkward than some might have expected."

After the meeting, Trump and his wife, Melania, met with Vice President-elect Mike Pence and House leader Ryan over lunch at the Capitol Hill Club. Ryan, whose relationship with Trump has also been rocky at times, showed the president-elect the future inaugural site from the vantage point of the speaker's balcony.

"We had a fantastic, productive meeting about getting to work, rolling up our sleeves, and going to work for the American people," Ryan told reporters afterward. "We are now talking about how we're going to hit the ground running to make sure that we can get this country turned around and make America great again."

Before the election, Trump regularly slammed Ryan on Twitter. At one point, Ryan called Trump's criticism of a Mexican-American judge the "textbook definition" of a racist comment.

Trump also plans to meet with Senate Majority Leader Mitch McConnell on Thursday afternoon, according to Politico.

As the transition begins, industry groups in Texas and elsewhere are preparing for the radically different policy agenda Trump is expected to pursue.

McConnell has said that repealing the Affordable Care Act will be high on the GOP agenda, while other Republican leaders have expressed confidence in substantially different administration policies in the realm of immigration and environmental regulation, among other issues.